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The issue of non‐linear robust state estimation in the integration of a strapdown inertial navigation system and global positioning system is addressed in this study. Based on the cubature Kalman filtering frame, a non‐linear robust filter called a robust cubature Kalman filter (RCKF) was introduced to address the outliers and the inaccurate model. It has been found that the determination of an optimal restriction parameter is crucial for maintaining the robustness and accuracy of the non‐linear robust filter. Unfortunately, the value of this restriction parameter is always determined by experience. In this study, an iterative strategy was proposed to adaptively attain the optimal restriction parameter without much previous experience. To improve the computational stability of the iterative non‐linear robust filter, a singular value decomposition strategy was adopted simultaneously. Two case studies indicate that the iterative RCKF can achieve greater robustness and accuracy using the methodology discussed in this study.

Distributed polarization measurement is a significant way to evaluate polarization-maintaining fiber. It can assess the fiber's polarization preserving ability and locate internal defects and external perturbations of a long-distance PM fiber. Distributed polarization crosstalk of a fiber-optic polarization device accurately describes its time-dependent optical performance. Therefore, distributed polarization measurement technology can be used to predict and prevent the performance degradation and failure. However, the remaining shortcomings of existing measurement methods are low dynamic range, short measurement length, inadequate spatial resolution, and low diagnostic ability. This paper reviews recent advances in solving the above issues and presents ways to obtain high performances: a dynamic range > 90 dB, a measurement length > 10 km, a full range spatial resolution < 10 cm, and developments in time domain, frequency domain, and time-frequency domain diagnosis methods. All these high-performance techniques have led to more effective diagnosis of fiber optic sensing coils. This can be demonstrated by a series of comparative measurements and analysis of three PM fiber optic sensing coils in various configurations such as a randomly-wound spool of fiber and a free-standing coil quadrupole-pattern-wound from it, a second coil with and without a flange at various temperatures, and a third coil spliced to a Y waveguide. Each is one of the key configurations during the production processes or the application of the fiber sensing coil. The technical progress reviewed here will greatly promote the development, production, and application of fiber sensing coils.

Polarization extinction ratio (PER) is a quantitative indicator of the polarization-maintaining (PM) ability of a device. In this work, we present a distributed PER measurement method based on white-light interferometry. It can accurately measure the PER distribution of a PM device even in the presence of strong polarization crosstalk. We show that the distributed PER can be expressed as the reciprocal of the accumulated polarization crosstalk along the device. Thus, the PER distribution of a PM device can be calculated from the distributed polarization crosstalk. In the presence of strong polarization crosstalk, we introduced a concept of polarization crosstalk induced loss to prove that there is a significant error of the measured distributed polarization crosstalk. The error can be accurately estimated and be calibrated out from the measurement result. To verify the measurement method and the calibration accuracy, we used a commercial PER meter that can only measure the total PER of a device as the reference. We simulated a quasi-distributed PER device under test (DUT) by successively splicing 15 pieces of PM fibers and measured its total PER after splicing each piece of fiber. The calculated distributed PER of the DUT after error calibration matches well with the quasi-distributed result at the corresponding locations. Finally, we applied the method to measure the distributed PER and total PER of a PM fiber coil. After error calibration, the residual error (i.e., the difference with the commercial PER meter) in the total PER, thus of the distributed PER, is less than 0.1 dB.